Counterexamples for the fractal Schrödinger convergence problem with an intermediate space trick
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866915133325836288 |
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| author | Eceizabarrena, Daniel Ponce-Vanegas, Felipe |
| author_facet | Eceizabarrena, Daniel Ponce-Vanegas, Felipe |
| contents | We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same regularity as Du's counterexamples for weighted $L^2$ restriction estimates is achieved for the convergence problem. To do so, we need to construct the set of divergence explicitly and compute its Hausdorff dimension, for which we use the Mass Transference Principle, a technique originated from Diophantine approximation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_04050 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Counterexamples for the fractal Schrödinger convergence problem with an intermediate space trick Eceizabarrena, Daniel Ponce-Vanegas, Felipe Analysis of PDEs Classical Analysis and ODEs Primary 35J10, Secondary 42B37 We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same regularity as Du's counterexamples for weighted $L^2$ restriction estimates is achieved for the convergence problem. To do so, we need to construct the set of divergence explicitly and compute its Hausdorff dimension, for which we use the Mass Transference Principle, a technique originated from Diophantine approximation. |
| title | Counterexamples for the fractal Schrödinger convergence problem with an intermediate space trick |
| topic | Analysis of PDEs Classical Analysis and ODEs Primary 35J10, Secondary 42B37 |
| url | https://arxiv.org/abs/2112.04050 |